I have some issues with Kokai.

First and foremost, I don't really feel like he's a "Better Generations" character as much as he's just fit to the Naruto theme in general. I know his history is not made, but I really don't see any plot elements or aspects of Birth of a Better Generation inside the character design. He also feels slightly like the Gary Sue type of Loyal Clansmen archetype, which would be fine, but that entire archetype has been influenced by the [u]mass genocide[/u] of every clan, very notably Konohagakure. On that note, even though there is pride in being a clan member, you have to realize this is only a set few years after every clan member was in hiding from Sai, who was selectively killing them. I would say that because of that alone, his training would be stunted greatly. Lastly, I do not personally mind using elemental jutsu on a Hyuuga, but there are four jutsu, some used by Jounin and S-Class ninja. Even if they scaled up, you have to realize that genin don't even learn most elemental jutsu at their stage. Sasuke was a prodigy and knew a handful of fire jutsu, and he was from one of the most prodigious clans of the series. I feel like you should reduce the jutsu to maybe one or two. I said six was the limit for genin; I did not say that having less would be less. 

Overall, I want the character more cemented into the setting and I want the Wind Release scaled back greatly. If you still want jutsu for Wind Release, make some custom ones that are relatively weak, but useful in terms of utility. Don't limit yourself to the pre-existing pool.